Monitoring and Analysis of a Bridge with Partially Restrained Bearings

This paper reports on the monitoring and analysis of a two-span bridge in which the bearings were partially restrained. In an earlier experimental study, it was shown that the natural frequencies changed in colder weather, and it appeared that this was due to restraints in the end bearings. This research was conducted to verify this initial conclusion and to develop an analytical approach based on the finite-element method to model this change. Additional field measurements were made. The nonlinear dynamic finite-element analysis is based on a planar model that includes the influence of both the deck cracking and the eccentric axial forces, which develop when the bearings are restrained. Both the flexural and the torsional modes are evaluated. Although the changes in the bearings and the overall structural behavior were relatively small, the results show that it was nevertheless possible to verify the changes with a nonlinear dynamic finite-element analysis calibrated with field measurements.     

Spatial Stability of Shear Deformable Nonsymmetric Thin-Walled Curved Beams: A Centroid-Shear Center Formulation

An improved shear deformable curved beam theory to overcome the drawback of currently available beam theories is newly proposed for the spatially coupled stability analysis of thin-walled curved beams with nonsymmetric cross sections. For this, the displacement field is introduced considering the second order terms of semitangential rotations. Next the elastic strain energy is newly derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. Then the potential energy due to initial stress resultants is consistently derived with accurate calculation of the Wagner effect. Finally, equilibrium equations and force–deformation relations are obtained using a stationary condition of total potential energy. The closed-form solutions for in-plane and out-of-plane buckling of curved beams subjected to uniform compression and pure bending are newly derived. Additionally, finite-element procedures are developed by using curved beam elements with arbitrary thin-walled sections. In order to illustrate the accuracy and the practical usefulness of this study, closed-form and numerical solutions for spatial buckling are compared with results by available references and ABAQUS’ shell elements.     

Effect of Friction on Shear Connection in Composite Bridge Beams

In the design of new composite steel and concrete bridge beams, the shear connectors are assumed to transmit all of the longitudinal shear forces at the interface between the concrete slab and the steel beam. However, in practice, the forces on the shear connectors are modified by friction resistances at the interface. The effect of friction on the fatigue endurance of shear connectors is first illustrated through a specially developed finite-element analysis procedure. Then a simple mathematical assessment model is proposed that allows for the beneficial effect of friction on the fatigue endurance of shear connectors in composite steel and concrete bridge beams. This procedure can extend the design life of the shear connectors in existing composite bridge beams, as it can be used to estimate their remaining endurance and their remaining strength and, if necessary, to determine the effect of remedial work on increasing the endurance of the shear connectors.     

Numerical Investigation of Creep Effects on FRP-Strengthened RC Beams

Numerical analysis using a finite-element model was performed to simulate and investigate the long-term behavior of two RC beams with similar steel reinforcement, cast from the same batch of concrete. One beam was a plain RC beam and the other beam was strengthened using carbon fiber-reinforced polymer (FRP) strips. The deflections of both beams have been monitored for 5 years after loading. The finite-element model included both creep of concrete and viscoelasticity of the epoxy adhesive at the concrete-carbon FRP (CFRP) interface. The results of the finite-element analysis are compared to experimental observations of the two beams. The finite-element analysis was found to be able to simulate the long-term behavior of the CFRP-strengthened beam and help us understand the complex changes in the stress state that occur over time.     

Torsional Stiffness of Prestressing Tendons in Double-T Beams

When a prestressed double-T beam is subjected to torsion, a pair of prestressing tendons resists torsional rotation because of the restoring action of the displaced prestressing tendons. A comprehensive formulation to account for the torsional restoring action of double-T beams is presented, based on Vlasov’s hypothesis of considering warping displacement in an open-section. The deformation energies of prestressing tendons and reinforcing bars are calculated based on the deformed geometry to obtain the total potential energy. A two-noded beam element with seven degrees of freedom per node approximates an axial displacement, two translations, two flexural, and one torsional rotations, and a warping displacement to derive the finite-element equilibrium equations by minimizing the potential energy function. The role of prestressing forces of the tendons on the torsional resistance and the limitations of the traditional transformed section approach are addressed when it is applied to torsional problems. As a numerical example, an existing three-span continuous double-T beam is analyzed, and the bimoment and angle of twist are compared to those calculated using conventional three-dimensional finite-element analysis and the analytical solution of governing differential equations.     

Finite Beam Element Considering Shear-Lag Effect in Box Girder

A finite-element method considering the interaction of the bending and shear-lag deformation of a box girder was established. Meanwhile a shear-lag-induced stiffness matrix was defined. The stiffness matrices considering the effect of the shear lag were deduced. At each node of the beam element, two shear-lag degrees of freedom were used as boundary conditions for the box girders. The proposed formulations were then applied to analyze the effects of the shear lag on the deflection, the internal forces, and the shear-lag coefficients in the simply supported cantilever and continuous box beams under uniformly distributed and concentrated loads. The numerical results obtained using the proposed procedure were in good agreement with those using the finite-shell-element method, the finite-stringer method, the analytical method based on the variational principle, and the model tests. The proposed method is reliable and more effective for the analysis of the shear lag in the actual box-girder structures.     

Numerical Model for Tracing the Response of FRP-Strengthened RC Beams Exposed to Fire

This paper presents the development of a numerical model for evaluating the performance of fiber-reinforced polymer (FRP)-strengthened RC beams under fire conditions. The model is based on a macroscopic finite-element approach and utilizes moment-curvature relationships to trace the response of insulated FRP-strengthened RC beams from linear elastic stage to collapse under any given fire exposure and loading scenarios. In the analysis, high temperature properties of constitutive materials, load and restraint conditions, material and geometric nonlinearity are accounted for, and a realistic failure criterion is applied to evaluate the failure of the beams. The model is validated against fire test data on FRP-strengthened RC beams and is applied to study the effect of FRP-strengthening, insulation scheme, and failure criterion on the fire response of FRP-strengthened RC beams. Results from the analysis indicate that FRP-strengthened RC beams should be protected with supplemental fire insulation to satisfy fire resistance requirements. A case study is presented to illustrate the application of the model for optimizing the fire insulation scheme to achieve required fire resistance in FRP-strengthened concrete beams.     

Equivalent Barge and Flotilla Impact Forces on Bridge Piers

Bridge piers located in navigable inland waterways are designed to resist impact forces from barges and flotillas in addition to other design considerations (e.g., scour dead, live loads, etc.). The primary design tool for estimating these forces is the AASHTO Guide Specification that provides a simple hand calculation method to determine an “equivalent impact force.” The simplicity comes at a cost of excluding the effect of the pier shape, impact duration, and interaction between barges in a flotilla. The objective of this paper is to present a hand calculation method for determining barge or flotilla impact forces on bridge piers. The primary advantage of this approach lies in its incorporation of pier geometry, interaction between barges, and impact duration. The proposed method is derived from the conduct of hundreds of finite-element dynamic simulations of jumbo hopper (JH) barges and flotillas, made up of JH barges, impacting bridge piers. Results are presented and compared with those derived from the AASHTO method and detailed finite-element modeling.     

Intermediate Crack Debonding in FRP-Strengthened RC Beams: FE Analysis and Strength Model

Reinforced concrete (RC) beams strengthened in flexure with a bonded fiber-reinforced polymer (FRP) plate may fail by intermediate crack (IC) debonding, in which debonding initiates at a critical section in the high moment region and propagates to a plate end. This paper first presents a finite-element (FE) model based on the smeared crack approach for concrete for the numerical simulation of the IC debonding process. This finite-element model includes two novel features: (1) the interfacial behavior within the major flexural crack zone is differentiated from that outside this zone and (2) the effect of local slip concentrations near a flexural crack is captured using a dual local debonding criterion. The FE model is shown to be accurate through comparisons with the results of 42 beam tests. The paper also presents an accurate and simple strength model based on interfacial shear stress distributions from finite-element analyses. The new strength model is shown to be accurate through comparisons with the test results of 77 beams, including the 42 beams used in verifying the FE model, and is suitable for direct use in design.     

Evaluation of Floor Vibration in a Biotechnology Laboratory Caused by Human Walking

A floor supported on long-span beams, which was designed to accommodate bio research instruments, is evaluated for vibration induced by people walking. First, a brief review in vibration criteria is given. The variation of force time histories imposed by people’s feet on supporting objects is also discussed. Both beam and floor finite-element models are then used to simulate the local walking response of the floor mathematically. Footfall forces are applied to the finite-element models via triangular distribution function. A comparison of the time history analysis results with the vibration criteria shows that the floor performs well under people walking. Field measurements were also conducted after the completion of the construction. The measured results show a good correlation with the finite-element analysis results. During the analyses, it was also found that as long as the local floor model covers a structural bay, the boundary conditions of the floor model do not affect the response much. Using an equivalent constant footfall force function can produce similar results compared with those obtained using a more sophisticated force function.     

Response and Analysis of Steel Trusses for Fatigue Truck Loading

The strain responses of several members of two different types of truss bridges to known truck loads are measured and compared to the responses calculated using typical structural analysis as well as 2D and 3D finite-element analysis. The simple calculations result in calculated stress ranges that significantly exceed the measured stress ranges in most cases, for many reasons including (1) flexural moments are carried by the deck; (2) trusses act in a way that is partially composite; (3) simple angle end corrections of floor beams act partially restrained; and (4) steel bearings on older large trusses typically do not respond to live loads like rollers. Typical ratios of the measured stresses to calculated stresses are developed for different parts of the superstructure if there is still a significant discrepancy after making reasonable refinements in the assumptions and analysis.     

Simple Degenerate Formulation for Large Displacement Analysis of Beams

A finite-element formulation for the large displacement analysis of beams is proposed. It is based on the degeneration approach: The governing equations for a general solid are directly discretized. The assumptions of the Timoshenko beam theory are implemented in the discretization process by devising beam elements and utilizing the penalty method. The formulation for 2D beam analysis is first presented and the 3D formulation follows. Characteristically, the proposed beam elements possess relative nodes and rotations are excluded from nodal variables. The beam formulations thus developed are quite simple and straightforward. It is noteworthy that unlike conventional formulations, the present formulation for 3D beam analysis is just a simple extension of the 2D case, which can be attributed mainly to the avoidance of rotations in nodal variables. In numerical examples, the approximate penalty number is investigated first by analyzing a cantilever beam, and it turns out to be 103 times Young's modulus. With this value, example problems are solved and excellent agreement with the existing solutions is observed, confirming the validity of the present formulation.     

Second-Order Sensitivities of Inelastic Finite-Element Response by Direct Differentiation

In this paper analytical equations are developed and implemented to obtain second-order derivatives of finite-element responses with respect to input parameters. The work extends previous work on first-order response sensitivity analysis. Of particular interest in this study is the computational feasibility of obtaining second-order response sensitivities. In the past, the straightforward finite difference approach has been available, but this approach suffers from serious efficiency and accuracy concerns. In this study it is demonstrated that analytical differentiation of the response algorithm and subsequent implementation on the computer provides second-order sensitivities at a significantly reduced cost. The sensitivity results are consistent with and have the same numerical precision as the ordinary response. The computational cost advantage of the direct differentiation approach increases as the problem size increases. Several novel implementation techniques are developed in this paper to optimize the computational efficiency. The derivations and implementations are demonstrated and verified with two finite-element analysis examples.     

Numerical Modeling of FRP Shear-Strengthened Reinforced Concrete Beams

An attractive technique for the shear strengthening of reinforced concrete beams is to provide additional web reinforcement in the form of externally bonded fiber-reinforced polymer (FRP) sheets. So far, theoretical studies concerning the FRP shear strengthening of reinforced concrete members have been rather limited. Moreover, the numerical analyses presented to date have not effectively simulated the interfacial behavior between the bonded FRP and concrete. The analysis presented here aims to capture the three-dimensional and nonlinear behavior of the concrete, as well as accurately model the bond–slip interfacial behavior. The finite-element model is applied to various strengthening strategies; namely, beams with vertical and inclined side-bonded FRP sheets, U-wrap FRP strengthening configurations, as well as anchored FRP sheets. The proposed numerical analysis is validated against published experimental results. Comparisons between the numerical predictions and test results show excellent agreement. The finite-element model is also shown to be a valuable tool for gaining insight into phenomena (e.g., slip profiles, debonding trends, strain distributions) that are difficult to investigate in laboratory tests.     

Mixed Finite Element for Three-Dimensional Nonlinear Dynamic Analysis of Rectangular Concrete-Filled Steel Tube Beam-Columns

A beam finite-element formulation following Euler-Bernoulli beam theory is presented for geometrically and materially nonlinear analysis of rectangular concrete-filled steel tube (RCFT) beam-columns. The formulation is geared for conducting transient dynamic analysis of composite steel/concrete frame structures. The element stiffness and internal forces were derived through adopting a mixed finite-element approach based on the Hellinger-Reissner variational principle. The load transfer between the steel and concrete constitutive materials was provided through steel and concrete interface via friction and interlocking. Six extra translational degrees-of-freedom (DOFs) were added to the conventional 12 DOF beam element to quantify the differential displacement between the two media. The formulation was verified for a range of geometrically nonlinear test problems and geometrically and materially nonlinear RCFT experimental test specimens from the literature. Strong correlation and convergence characteristics were achieved compared to the published results.     

Analytical and Experimental Study of Lateral and Distortional Buckling of FRP Wide-Flange Beams

A combined analytical and experimental evaluation of flexural-torsional and lateral-distortional buckling of fiber-reinforced plastic (FRP) composite wide-flange (WF) beams is presented. Based on energy principles, the total potential energy equations for instability of FRP WF sections are derived using the nonlinear elastic theory. For the analysis of lateral-distortional buckling, a fifth-order polynomial shape function is adopted to model the deformed shape of web panels. The models are validated by testing two geometrically identical FRP WF beams but with distinct material architectures produced by the pultrusion process. The beams are tested under midspan concentrated loads to evaluate their flexural-torsional and lateral-distortional buckling responses. To detect rotations of the midspan cross sections and onset of critical buckling loads, horizontal transverse bars are attached to the beam's flanges, and the bar ends are connected to linear variable differential transducers (LVDTs). For the same purpose, we use strain gauges bonded to the upper and lower surfaces near to the free edges of the top flange. A good agreement between the proposed analytical approach and experimental and finite-element analyses results is obtained, and simplified engineering equations for flexural-torsional buckling are formulated. The proposed analytical solutions can be used to predict flexural-torsional and lateral-distortional buckling loads for other FRP shapes and to formulate simplified design equations.     

Mechanics of Composite Sinusoidal Honeycomb Cores

Lightweight and heavy-duty fiber-reinforced polymer (FRP) composite honeycomb sandwich structures have been increasingly used in civil infrastructure. Unique cellular core configurations, such as sinusoidal core, have been applied in sandwich construction. Due to specific core geometry, the solutions for core effective stiffness properties are not readily available. This paper presents a mechanics of materials approach to evaluate the effective stiffness properties of sinusoidal cores. In particular, the internal forces of a curved wall in a unit cell are expressed in terms of resultant forces, and based on the energy method and principle of equivalence analysis, the in-plane stiffness properties of sinusoidal cores are derived. Both finite-element modeling and experimental testing are carried out to verify the accuracy of the proposed analytical formulation. To illustrate the present analytical approach as an efficient tool in optimal analysis and size selection of sinusoidal cores, several design plots are provided and discussed. The simplified analysis and formulation presented for sinusoidal cores can be used in design application of FRP honeycomb sandwich and optimization of efficient cellular core structures.     

Use of Mixed-Mode Fracture Interfaces for the Modeling of Large-Scale FRP-Strengthened Beams

In this study, numerical models of fiber-reinforced polymer (FRP)-strengthened beams were developed using nonlinear fracture mechanics for the modeling of the concrete-FRP (longitudinal and U-wrap) interfaces. Mode 1, Mode 2, and mixed-mode interfacial behaviors were considered. Results from the finite-element models were compared with experimental tests of large-scale strengthened beams using FRP U-wraps as anchors. The numerical program assessed the effect of the interfacial modeling in the global and local responses. A parametric study was conducted to determine the effect of additional longitudinal FRP sheets in strengthened beams with and without FRP U-wraps. Results from this study indicate that the use of a mixed-mode concrete-FRP interface is a robust numerical approach for the prediction of the global and local responses of large-scale FRP-strengthened beams. The parametric study shows that the use of FRP U-wraps could improve the strength and ductility of the FRP-strengthened beams by changing their failure mode and deflection response. Appropriate modeling of the concrete-FRP interfaces is needed to successfully predict these effects.     

Flexural Strengthening of RC Beams with Externally Bonded CFRP Systems: Test Results and 3D Nonlinear FE Analysis

This paper presents experimental results and a numerical analysis of the reinforced concrete (RC) beams strengthened in flexure with various externally bonded carbon fiber-reinforced polymer (CFRP) configurations. The aim of the experimental work was to investigate the parameters that may delay the intermediate crack debonding of the bottom CFRP laminate, and increase the load carrying capacity and CFRP strength utilization ratio. Ten rectangular RC specimens with a clear span of 4.2?m, categorized in two series, were tested to evaluate the effect of using the additional U-shaped CFRP systems on the intermediate crack debonding of the bottom laminate. Two different configurations of the additional systems were proposed, namely, continuous U-shaped wet layup sheets and spaced side-bonded CFRP L-shaped laminates. The fiber orientation effect of the side-bonded sheets was also investigated. A numerical analysis using an incremental nonlinear displacement-controlled 3D finite-element (FE) model was developed to investigate the flexural and CFRP/concrete interfacial responses of the tested beams. The finite-element model accounts for the orthotropic behavior of the CFRP laminates. An appropriate bond-slip model was adopted to characterize the behavior of the CFRP/concrete interface. Comparisons between the FE predictions and experimental results show very good agreement in terms of the load-deflection and load-strain relationships, ultimate capacities, and failure modes of the beams.     

FE Modeling of FRP-Repaired Planar Concrete Elements Subjected to Monotonic and Cyclic Loading

In this paper, a nonlinear finite-element model is developed for the analysis of plane stress members, such as RC beams and walls, strengthened either unidirectionally or bidirectionally with fiber-reinforced polymer (FRP) composites and subjected to either monotonic or cyclic loading. The model takes into account the effects of the bonded interface between the FRP and concrete while allowing slippage in each direction. A two-dimensional membrane contact element is developed to model the effects of local bond-slip with debonding failure between the FRP and concrete capable of being captured. The model has been incorporated into a finite-element program for the analysis of RC members subject to plane stress with verification against test data of FRP-strengthened RC joints, beams, and walls. The numerical results show good agreement with the experimental data for both load-displacement responses and for the overall failure mechanisms.